in triangle ABC, the size of angle B is 5 times the size of angle A and the size of angle C is 9 degrees less than 4 times the size of angle A
Find the size of angle A
You can set up the equations as follows:
B=5A
C=4A-9
A+B+C=180 (sum of angles of a triangle).
and solve for A, B and C.
However, you can easily solve it by substitution into the third equation:
A+B+C=180
A + 5A + 4A-9 = 180
10A=189
A=18.9
With A known, you can then find the remaining angles by substitution into the first two equation.
The sum of the angles of a triangle are 180 degrees.
Therefore:
Let x = angle A
5x = angle B
4x - 9 = angle C
Equation:
x + 5x + 4x - 9 = 180
Solve for x.
Let's assume the size of angle A is x degrees.
Given that angle B is 5 times the size of angle A, angle B = 5x degrees.
Also, angle C is 9 degrees less than 4 times the size of angle A, angle C = (4x - 9) degrees.
In a triangle, the sum of all angles is 180 degrees. So, we can set up an equation:
Angle A + Angle B + Angle C = 180
Substituting the values we found:
x + 5x + (4x - 9) = 180
Simplifying the equation:
10x - 9 = 180
Adding 9 to both sides:
10x = 189
Now, solving for x by dividing both sides by 10:
x = 189 / 10
x ≈ 18.9
Therefore, the size of angle A is approximately 18.9 degrees.
To find the size of angle A, let's assume that angle A is represented by x degrees.
We are given that the size of angle B is 5 times the size of angle A. Therefore, the size of angle B is 5x degrees.
We are also given that the size of angle C is 9 degrees less than 4 times the size of angle A. Therefore, the size of angle C is 4x - 9 degrees.
In a triangle, the sum of all angles is always 180 degrees.
So, we can write the equation:
Angle A + Angle B + Angle C = 180
Substituting the values we have:
x + 5x + (4x - 9) = 180
Simplifying the equation:
x + 5x + 4x - 9 = 180
10x - 9 = 180
10x = 189
x = 189/10
x = 18.9
Therefore, the size of angle A is 18.9 degrees.